Question

11. You've been asked to build a machine for a TV commercial that launches soda bottles from ground level over a volleyball net. You estimate the soda needs to clear at least 8 feet in order to sail over the net. The equation that represents the height of the bottle as a function of time (t) in seconds is: h= -16t2 + 30.4t How many times does the soda cross the 8 foot threshold? O 2 O 1 Oo

Answer 1

h = -16t^2 + 30.4t

To estimate the number of times the soda crosses the 8-foot threshold, set the height h = 8 and solve for t.

-16t^2 + 30.4t = 8

16t^2 - 30.4t +8 = 0

2t^2 - 3.8t + 1 = 0

Using quadratic formula,

t = [ 3.8 ± sqrt ( (-3.8)^2 - ( 4 * 2 * 1) ) ] / (2*2) = (3.8 ± sqrt(6.44)) / 4 = (3.8 ± 2.54)/4

t = 1.584 or t = 0.316

Both values of time are reasonable.

So the soda crosses the 8-foot threshold 2 times.

Answer is 2.